Ha! I actually kinda' like the over-dubbed vox effect smile

But, yes... you do need at least a vocal mic! I have the ZOOM R24 version of your Tascam which I basically use as a pre-mixer/interface for my computer. The built in stereo mics alone are great for recording acoustic guitar, but I like the effect you're getting with your amp! Those mics do OK for "roomy background" vox, but you do need a mic to punch out your lead vox.

https://www.shure.com/en-US/products/microphones/sm58

I've used an old Shure Prologue for more than 30yrs because, when I bought it, I couldn't afford the SM58 LOL smile